Precisely cyclic sand: Self-organization of periodically sheared frictional grains

Abstract

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain-friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many-degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic.granular | self-organization | limit cycles | friction S elf-organization under periodic driving is a common feature in many disparate far-from-equilibrium systems (1-4). Recently, there has been substantial interest in self-organization in suspensions under slow, cyclic, low-Reynolds number shear (1, 5, 6). Non-Brownian suspensions were found to exhibit a phase transition from a dynamic fluctuating state to a reversible absorbing state depending on the shear amplitude and particle density. Here, there is a clear route to reversibility, because at low Reynolds numbers the equations of motion for the fluid are reversible, and irreversibility is only introduced through particle collisions or potential interactions. A similar cyclic behavior has been observed in periodically driven superconducting vortices (4), which interact via a nonlinear potential.If one instead considers a pack of frictional grains, this picture changes dramatically and the conditions for reversibility/irreversibility and periodic motion remain poorly understood (7-9). Here, the equations of motion are not time-reversible and particles remain in contact with their neighbors at all times, interacting via hysteretic frictional forces instead of simple collisions. Although a priori the system is hysteretic and irreversible, it is still possible to exhibit correlations and self-organization. Indeed, experimental studies of grains under cyclic shear have found spontaneous crystallization (10, 11), dynamic heterogeneities (12), and subdiffusive caged motion (9, 13). Recent experiments on 2D frictional disks found limit cycles in the shear stress and pressure in shear-jammed packings (14), although the individual grain motion remains diffusive. However, experiments are limited to a narrow range of friction and one cannot easily vary this crucial parameter that determines the possible packing configurations (15) and the response of the granular system to applied shear. Although we do not find reversible states, we do find that, depending on the strain amplitude and grain friction, the granular system can organize itself and evolve i...

Embedding orthogonal memories in a colloidal gel through oscillatory shear

“…Further studies have argued that this oscillatory shear memory effect should apply to disordered systems in generalshearing causes rearrangement which continues until a reversible state is found [6][7][8]. Indeed, similar memory effects have been found in experiments and simulations of model amorphous systems [2,9,10], granular systems [11], and glasses [12][13][14][15]. The interactions between particles can vary and even the nature of the reversibility can vary for different systems [9,[16][17][18][19][20].…”

Memory formation in cyclically deformed amorphous solids and sphere assemblies

“…The presence of multiple distinct internal structures or states in which a material can exist for long times is a generic condition for the presence of memory effects, seen particularly in systems that exhibit some form of disorder. The range of examples is vast, and includes structural glasses [2][3][4][5] and spin glasses [6], magnetic systems with disorder [7][8][9][10][11] that exhibit return point memory, and charge density waves systems that exhibit return point memory and pulse duration memory [12][13][14][15][16][17][18][19], crumpled thin sheets and elastic foams [20], systems exhibiting echoes [21], sheared colloidal suspensions [22][23][24], glasses and related model systems [25][26][27], and shaken granular systems [28][29][30], to name a few examples. This list of largely condensed matter examples does not include the large array of biological contexts in which memory formation is important and interesting, such as neuronal, genetic, epigenetic, immunological etc.…”

Reversible to irreversible transitions in periodically driven skyrmion systems

“…Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the colloidal particles, such as granular matter [18][19][20][21], dislocations [22,23], amorphous solids [24][25][26][27], polycrystalline solids [28], charged colloids [29], and vortices in type-II superconductors [30][31][32]. The dynamics of most of these systems is overdamped, and little is known about how nondissipative dynamics would affect a reversible to irreversible transition.…”